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HAEMONY: 


ISTORIC  POINTS  AND  MODERN  METHODS 
OF  INSTRUCTION. 


BY    E.    M.    BOWMAN. 

I' 


CINCIXNATI: 
PUBLISHED  BY  JOHX  CHUECH  &  CO., 

No.  CC  West  Fourth  Street. 

COPYRIGHT,  1881,  BY  J.  CHURCH  &l  CO. 


^ 


>^^ 


i 


All~4ro 


HARMONY: 

HISTORICAL  POINTS  AND  MODERN  METHODS  OF 
INSTRUCTION. 


It  h  not  probable  that  harmony  was  employed  prior  to  the  ninth 
century,  except  perhaps  in  the  music  of  the  spheres. 

Up  to  that  period,  Psalms  and  Hymns  were  sung  in  unison, 
notwithstanding  the  already  known  possibility  of  simultaneously 
uniting  different  sounds. 

Dr.  Ritter  says,  in  his  valuable  epitome  of  Musical  History,  "  The 
oldest  historical  document  of  which  we  have  any  knowledge,  on 
harmony,  in  the  modern  acceptation  of  the  term,  is  by  ^Isidore, 
Archbishop  of  Seville,  who  lived  at  the  time  of  St.  Gregory  (from 
570  to  636  A.  D.),  and  whose  friend  he  was.  Isidore  says,  in  his 
'Sentences  on  Music,'  'Harmonious  music  is  a  modulation  of  the 
voice :  it  is  also  the  union  of  simultaneous  sounds.'  He  also  speaks 
of  two  kinds  of  harmony,  Si/mphony  and  Diajohomj.  By  the  first 
word  he  meant  probably  a  combination  of  consonant,  and  by  the 
latter  oi  dissonant  intervals." 

It  seems  certain  that  the  earliest  efforts  in  part-singing  were  in 
fourths, -fifths  and  octaves.  Ilucbald,  a  Flemish  monk  who  lived,  ac- 
cording to  Fetis,  from  about  840  to  932  a.  d.,  was  the  first  theoreti- 
cal writer  of  eminence.  He  left  a  treatise  on  harmony,  or,  as  it 
was  then  called,  Organum  or  Diaphony,  entitled  "Enchiridion 
Musioiie,"  in  which  rules  and  examples  are  given  for  the  proper 
progression  of  the  different  parts  or  "  symphonies,"  as  they  were 
then  termed. 

1I«^  made  use  of  consonant  fourths,  fifths  and  octaves,  almost  ex 

(3) 

383380 


[4] 

clusively,  Stiid  to  secure- such  intervals,  chromatic  alterations  were 
made  wherever  necessary. 

Here  is  an  example  of  Hucbald's  style  of  composition,  in   the 
Dorian  mode. 


:^2ZiSE§=^E§=^Egz:22:_^_ 


"2?~~2^~C?~~2^~C?~~^='~:S.  ^.  JLL 


-t^- 


-C^- 


And  here  is  another  in  which  occur  chromatic  alterations  nec- 
essary to  securing  consonant  fourths  and  fifths : 


.^.   -^   .^- 

2. 

j^.    -«2.     (^      r2     .G      r^      r2      ^-2. 

"                                                                                                                                                                                                                   i 

r^^  -g-->^  -gl 

-g-  -g-  -g-  -^  -g^^  ^^  <=  ^  ^ 

-^—^—^—■r^—rzrW^-^^ —-^-^^  - 

"S^  '=^'    <^  k^^     r^ 

Ilucbald  is  also  known  to  have  used  major  sixth?,  and  here  is  an 
example  in  Avhich  there  are  mf\jor  thirds,  also,  and  here  we  Lave 
the  origin  of  passing-notes  :- 


3. 

^    .^    ^-    :?:    ^ 


pE: g2Z=gzz:^z^g:2zizg2^zg:2:zz2^i^  j 


It  is  almost  incredible  to  us.  of  the  present  day  that  a  series  of 
fifths  and  octaves  could  ever  have  been  regcvrdod  as  an  improve- 
ment on  the  unison. 

But  it  evinces  their  first  flight  after  something, — they  knew  not 
what,  and  it  is  more  than  probable  that  if  the  brilliancy  of  the 
present  development  of  that  something  could  have  been  flashed 
into  their  figuratively  blind  eyes  and  deaf  ears,  they  would  have 
been  overwhelmed  and  have  shrunken  back  into  their  monk's 
cowls  and  thought  their  beloved  Organtim  divinely  more  beautiful. 

A  century  later  Guido  essayed  to  improve  upon  Hucbald,  but  left 
nothing  more  advanced  than  the  example  I  have  just  given.     The 


[5] 

Organum  or  Diaphony  of  this  era  was  succeeded,  before  Guido'a 
death,  by  the  primo-genitor  of  Counterpoint,  viz:  Discantus. 

It  has  been  suggested  that  it  probably  originated  as  a  musical 
trick,  by  adapting  two  different  melodies  to  each  other.  The  princi- 
ple involved,  however,  sprang  quickly  into  favor  for  church  pur- 
poses, and  Franco  of  Cologne,  who  also  made  important  improve- 
ments in  our  system  of  mensural  music,  christened  it  Discantus,  or 
Discant,  i  e.,  Double-song,  and  gives  us  a  description.  He  divides 
the  consonances  into  three  classes: — perfect  (the  octaves),  mld.Ue 
(fourths  and  fifths)  and  imperfect  (the  major  and  minor  thirds). 

He  classes  sixths  among  the  dissonances,  but  regards  their  use 
in  Discant  as  more  agreeable  than  minor  seconds,  sharp-fourths, 
sharp-fifths  and  sevenths.  Franco  also  exhibits  the  first  symptoms 
of  nausea  at  the  fifth  and  octave  successions  of  his  predecessors, 
saying  that  an  interchange  of  perfect  and  imperfect  consonances 
is  better  than  a  continued  succession  of  either. 

Following  the  Discant,  in  the  middle  ages,  there  sprang  up  a 
kind  of  harmony  known  as  Faux  Bourdon  or  Falso-bordone,  a  sim- 
ple sort  of  counterpoint  to  the  Gregorian  chant. 

It  consisted  principally  in  a  sequence  of  chords  of  the  sixth  ac- 
companying the  cantus  Jirmus.     Here  is  an  excellant  example. 


I-f- 

4. 

. 

m= 

TNT"  ^^-^^—' cs-s*^*   as-j^  ^ 

This  style  was  regarded  by  many  as  altogether  too  trivial  for 
divine  service,  and  the  feeling  ran  so  high  that  Pope  John  XXII 
issued  a  decree  at  Avignon  calling  on  the  clergy  to  return  to  their 
first  love,  the  Organum,  and  not  to  be  led  away  by  the  disciples  of 
the  new  school  of  music,  allowing  their  ears  to  be  tickled  by  their 
semihreves  and  minims  and  such  like  frivolous  inventions,  instead  of 
maintaining  the  ancient  ecclesiastical  chant. 


[6] 

It  was  of  no  avail,  however,  for  the  falso-bordone  soon  invested 
even  the  pope's  chapel,  thus  paving  the  way  for  the  works  of  the 
many  bright  lights  who  wrote  later  for  .the  Catholic  church.  Gaf ar- 
ias (1431-1522)  and  Adam  da  Fuldu,  of  about  the  same  period,  are 
among  the  earliest  writers  who  mention  this  kind  of  harmony. 

The  first  writers  of  eminence  outside  the  ecclesiastical  orders 
were  Marchdtus  of  Padua  and  de  Muris' oi  Paris.  Follow^ing  in 
Franco's  footsteps,  they  came  out  clearly  against  consecutive  fifths 
and  octaves,  Untrammeled  by  churchly  conservatism,  it  is  proba- 
ble that  they  wrote  and  experimented  more  freely  than  their  pre- 
decessors. Certain  it  is  that  Marchettus  is  the  author  of  chromatic 
progressions  which  Fetis  characterizes  as  "prodigiously  bold"  for 
that  era;  so  daring,  indeed,  that  they  were  not  adopted  until  long 
afterward.     Hero  is  an  excerpt : 

5. 

Marchettus  treats  also  of  dissonance?,  amongst  which  he  places 
fourths,  and  says  that  the  dissonant  voice  must  resolve  to  a  conso- 
nance, while  the  other  voice  remains  stationary, — a  decided  advance, 
certainly,  on  the  Organum  of  Ilucbald. 

De  Muris,  in  his  "xVrs  Contrapuncti,"  divides  the  consonances 
into  perfect  (fifths  and  octaves)  and  imperfect  (major  and  minor  thirds 
and  major  sixths)  which  shows  an  advance  from  Franco's  method. 

As  will  be  reaiarked,  the  7ninor  sixth  is  still  unrecognized.  In 
addition  to  directions  for  the  inter-mingling  of  perfect  and  imper- 
fect consonances,  he  adds  that  the  voices  should  not  ascend  or 
descend  in  fifths  or  octaves,  but  that  they  may  do  so  in  major  and 
minor  thirds  and  major  sixths. 

The  first  writer  of  importance  following  de  iMuris,  was  Dufay,  a 
Netherlander  born  about  1360,  from  whom  we  have  examples  in 
four-part  counterpoint  which  show  a  note-worthy  advance  on  any 
thing  recorded-  of  his  forerunners.  What  we  term  the  complete 
common  chord  occurs  frequently  in  Bufay's  composition,  also  the 


[7] 

so-called  First  Inversion,  or  chord  of  the  Third  and  Sixth.  The 
Second  Inversion,  or  chord  of  the  Fourth  and  Sixth,  did  not  appear 
until  later. 

Dufay  was  the  first  to  give  to  music  a  broad  basis.  He  wrote 
several  masses  and  secular  songs,  two,  three,  and  four-voiced,  show- 
ing remarkable  skill,  for  his  era,  in  the  imitative  style,  as  well  as 
marked  purity  in  the  harmony.  He  managed  the  dissonances  ar- 
tistically and  seems  to  have  realized  the  advantage  of  their  occur- 
ring unaccented  or  as  passing-notes. 

OcJcenhcim,  a  century  later,  occasionally  made  use  of  suspensions, 
as  for  example : 


S 


-m 


22: 


7^ 


Josquin  de  Pres  (born  about  the  middle  of  the  15th  century),  Ocken- 
heim's  most  celebrated  pupil,  is  said  by  Dr.  Ambros,  the  distin- 
guished German  historian,  to  have  been  the  first  to  make  use  of  a 
major  third,  in  the  final  chord,  instead  of  the  fifth,  a  bold  innovation, 
indeed. 

We  also  find  chromatic  alterations  in  his  cadences  which  give  us 
what  we  call  the  leading-tone,  thus  showing  an  advance  in  the  feel- 
ing for  tonality,  the  culmination  of  which,  we,  of  this  later  day, 
have  seen  in  the  overthrow  of  the  Ecclesiastical  Modes,  and  the 
elevation,  in  their  stead,  of  the  Major  and  Minor  tonalities.  Here 
is  an  illustration  in  point: 


r 


4N: 


^ 


1221 


The  custom  of  using  a  major  third  in  the  final  chord  of  a  composi- 
tion in  a  viiy^or  hey  became  almost  universal,  and  was  in  vogue  as 
late  as  Bach  and  Handel  and  even  Mozart.     These  latter,  however. 


I  8  ] 

used  the  major  or  minor  third  as  they  saw  fit,  but  in  the  older  com- 
positions, when  the  major  third  did  not  so  appear  in  the  final  chord, 
its  place  was  taken  by  a  bare  fifth,  according  to  the  still  older  rule 
respecting  cadences,  which  demanded  perfect  consonances,  alone, 
for  the  close,  thus  permitting  the  use  of  consonant  fifths  and  oc- 
taves, only. 

Here  is  an  example  of  Josquin's  use  of  the  major  third.  It  occurs 
at  the  conclusion  of  a  requiem  in  memory  of  his  revered  master 
Ockenheim. 


Palcstrlnas  epoch  (J521-94)  was  a  very  important  one.  Triads, 
passing-notes  and  dissonant  suspensions  abounded  in  his  works  and, 
indeed,  his  success  in  the  attempt  to  revivify  church  music,  is  said 
to  have  rested  chiefly  on  his  recognition  of  harmonic  principles. 
Many  passages  in  his  compositions  we  would  now  class  as  harmonic 
or  homophonic  rather  than  contrapuntal  or  polyphonic,  the  style 
of  writing  then  prevalent. 

The  actual  difference  in  the  two  methods  appears  to  be  that  in 
the  polyphonic  or  contrapuntiil  style,  the  chords  or  harmonies  are 
indicated  accidentally,  as  it  were,  by  the  interweaving,  impinging 
voice  parts,  while  in  the  homophonic  or  harmonic  style,  the  har- 
monies are  primary,  and  whole  movements  are  based  upon  their 


[91 

inter-dependent  relations,  and  unity  largely  secured  through  their 
grouping  into  keys. 

Owing  to  the  peculiar  construction  of  the  ecclesiastical  scales, 
there  was  a  vagueness  in  the  tonality  which  compelled  the  old  mas- 
ters to  employ  other  means  of  giving  to  their  works  unity  and 
connection.     This  they  found  in  canonic  imitation. 

Zarlino,  who  wrought  in  Palestrina's  era,  was  the  first  to  establish 
any  fixed  rules  for  harmony.  A  combination  of  tones  like  our 
chords  of  the  seventh  struck  him  as  noteworthy,  but  to  the  daring 
Moatevcrde  (1568-1043)  belongs  the  honor  of  inaugurating  the  mod- 
ern school  of  composition,  and  the  modern  treatment  of  dissonances. 
Up  to  his  time  the  Dominant  Seventh  had  only  been  heard  in  sus- 
pensions, or  as  a  passing-note.  He  originated  new  suspensions  of 
the  seventh  and  ninth,  and,  growing  bolder,  threw  off  the  yoke  of 
grey-bearded  contrapuntal  law  and  made  the  startling  innovation 
of  allowing  the  diminished  triad,  the  dominant  and  diminished 
seventh  and  the  ninth  to  enter  unprepared  (free). 

If  Monteverde  was  bold  with  the  entrance  of  his  dissonances, 
Frescabaldi,  a  contemporary  of  his,  was  equally  bold  in  their  res- 
olution, as  against  the  law  requiriag  all  dissonances  to  resolve 
downward. 

The  strife  between  the  old  and  new  schools  at  once  began,  but  a 
path  had  been  opened  which  led  to  new  beauties  at  every  turning, 
a  path  which  later  genuises  delighted  to  walk  in  or  explore,  and 
the  defeat  of  the  polyphonic  school,  with  its  own  peculiar  beauties 
and  the  glories  of  its  antiquity,  was  the  inevitable  result.  As  in 
every  revolution,  the  pendulum  swung  to  the  other  extreme  of  its 
arc,  and  composers,  in  looking  upon  the  harmonies  as  of  altogether 
paramount  importance,  lost  sight  of  that  other  very  important  ele- 
ment, the  progression  of  the  individual  parts.  ConseqMently,  it 
was  not  until  the  genius  of  Bach  and  Handvl  had  exerted  its 
mighty  influence,  molding  the  two  elements,  counterpoint  and 
harmony  into  helpful  union,  that  the  full  vigor  of  modern  music 
was  manifested. 

To  sketch  the  musical  history  of  eight  hundred  years  thus  briefly 


[10] 

has  necessarily  caused  the  omission  of  many  worthy  names,  but 
my  main  point  thus  far  has  been  simply  to  outline  the  course  of 
evolution  in  harmony  from  its  germinal  point,  or,  what  our  scien- 
tist friends  would  call  a  protoplasm,  on  and  up  through  its  various 
metamorphoses  to  that  stage  of  development  where  it  might  become 
interesting  and  profitable  to  speak  of  some  of  the  methods  of  in- 
struction. 

In  teaching  Harmony,  about  the  first  thing  which  we  all  take  up 
is  the  subject  of  Intervals;  the  pupil  must  be  thoroughly  inoculated 
with  Intervals  and  their  Inversions.  I  remember,  however,  that  I 
found  it  extremely  interesting,  in  my  first  lesson  from  Weitzman, 
to  follow  him  in  his  scheme  for  justifying  the  selection  of  tones 
which  we  use  in  our  musical  system. 

He  went  on  to  say  "if  we  vibrate  a  string  whose  fundamental 
pitch  is  F,  the  harmonics  or  overtones  will  be  the/  above,  then  c, 
/,  «,  etc.; 

"  A  single  vibrating  string,  or  column  of  air,  thus  generates  its 
octave,  fifth,  third,  etc.,  showing  Nature's  most  intimate  relation- 
ships. " 

"  Xow,  if  we  vibrate  another  string  half  as  long  as  the  first,  we 
would  have  the/,  c,/  a,  etc.,  an  octave  higher;  so  that  to  perpetuate 
the  octave  relationship  would  not  discover  to  us  all  the  tones  adopted 
in  our  tonal-system. " 

"  If  we  make  use  of  the  nest  most  intimate  relationship,  however, 
after  the  octave,  viz:  the  fifth,  a  string  sounding  C,  we  shall  come 
upon  new  tones  at  once,  the  harmonics  of  C  being  c,  g,  c,  c,  etc.  If 
we  perpetuate  this  process,  taking  the  fifth  at  each  change  of  string, 
the  result  will  be  the  chain  of  tones  forming  our  tonal-system,  each 
related  in  the  fifth  to  its  predecessor  and  successor,  as  follows  ": 

fcgdaeblfcgdaeblFCGDAEBjfcgdaeb   jfcgdaeb 

In  going  over  this  scheme,  the  student  will  also  readily  learn  the 
dominant  and  sub-dominant  of  any  given  tonic. 

Passing  on  to  the  subject  of  intervals  I  confess  that  I  approach  it 


[11] 

with  a  keen  appreciation  of  the  difForences  of  opinion,  which  miy, 
and  probably  do  exist  among  us,  especially  on  this  topic.  I  recog- 
nize the  fact  that  if  we  are  once  rooted  and  grounded  in  any 
certain  system  in  childhood  or  youth,  then  grow  up  on  it  and  teach 
it  year  after  j^ear,  the  almost  inevitable  result  will  be  the  formation 
of  a  prejudice,  which  is  as  much  a  part  of  us  as  is  the  hump  on  a 
camel's  back.  So,  if  there  are  differences  among  us,  if  dissonances 
do  appear,  let  us  lead  them  along  smoothly,  melodically,  and  finally 
resolve  them  amicably  to  consonances. 

Albrechtsberger,  and  most  other  modern  theorists,  classify  the 
consonances  into  perfect  and  imperfect,  just  as  de  Muris  did  in  the 
14th  century.  As  no  note  is  taken  of  their  difference  in  composi- 
tion now,  as  was  the  case  in  early  times,  this  doctrine  is  only  valua- 
ble historically. 

All  the  text-books  which  have  come  under  my  notice,  with  but 
one  or  two  exceptions,  agree  upon  five  classes  of  interval:  Perfect, 
Major,  Minor,  Diminished  (or  imperfect)  and  Augmented  (other- 
wise superfluous  or  extended.) 

It  would  simplify  matters  greatly  if  we  could  reduce  the  number 
of  kinds  of  interval,  and  I  can  discover  no  good  reason  why  we 
may  not  discard  the  word  "  Perfect,"  altogether,  and  say  in  its  place 
Major,  Minor,  Diminished,  and  Augmented. 

The  Perfect  4th  and  Perfect  5th  are  confessedly  not  perfect,  ac- 
cording to  our  Equal  Temperament  system,  and  to  call  them  so  is 
a  contradiction,  and  therefore  inconsistent. 

There  ought  to  be  adopted  in  common,  some  simple,  systematic 
formula  of  interval  nomenclature  which  would  do  away  with  the 
confusing  contradictions  of  the  various  methods  now  in  existence. 
In  addition  to  the  incongruity  of  the  whole  matter,  it  works  posi- 
tive injury  to  many  students,  those,  for  example,  who  can  not  or  do 
not  complete  their  studies  under  one  teacher.  They  get  fairly 
started,  get  accustomed  to  a  certain  method,  when,  for  some  reason 
they  change  teachers.  Teacher  No.  2  has  a  little  different  method, 
and  the  pupil  gets  them  confused.  The  result  too  often  is  that 
neither  method  ever  becomes  as  second  nature  to  him. 


[  12  ] 

We  learn  every  thing  by  analogy.  "We  use  a  known  thing  as  a 
stilt  to  help  us  up  to  something  as  yet  unknown.  Trace,  if  you 
please,  the  progression  by  which  a  pupil  arrives  at,  or  may  arrive  at, 
an  abstract  knowledge  of  intervals. 

In  childhood  he  first  takes  a  step  ;  he  then  learns  what  it  is,  its 
every  day  use,  a  movement  of  the  body  and  a  means  of  measure- 
ment. By  and  by  he  comes  to  study  Harmony  and  learns  what  the 
technical  meaning  of  a  step  or  half-step  is  as  applied  to  musical 
measurement.  By  analogy,  or  in  other  words  using  this  something 
already  known  to  discover  the  unknown,  by  counting  the  steps 
and  half-steps,  he  acquires  a  knowledge  of  each  major  interval. 

When  he  has  committed  this  knowledge  to  memory  he  is  ready 
to  proceed  farther.  By  analogy,  if  he  have  a  systematic  order  to 
go  by,  he  can  just  as  easily  learn  the  other  classes  of  intervals. 
Having  committed  the  compass  of  each  to  memory,  he  will  have 
acquired  an  abstract  knowledge  of  intervals,  so  easily  and  progres- 
sively that  he  will  almost  wonder  how  it  came  to  him. 

INVERSION  OF  INTERVALS. 

Inversion  is  frequently  defined  as  the  placing  of  one  or  the 
other  member  of  an«interval  an  octave  higher  or  lower. 

If  the  original  interval  were  greater  than  an  octave,  the  pro- 
cess defined  would  not  invert  but  simply  contract  the  interval. 

The  definition  should  call  for  the  inversion  or  turning  upside 
down  of  the  original  interval,  the  placing  of  the  lower  tone  above 
the  original  upper,  or  the  upper  tone  below  the  original  lower,  re- 
gardless of  the  distance  traversed. 

It  is  impossible  to  invert  a  prime,  because  in  that  interval  there 
is  no  lower  or  upper  tone  to  start  with,  and  to  change  an  octave 
into  a  prime  is  not  inversion,  because  the  lower  tone  does  not 
thereby  become  an  upper,  and  vice  versa.  This  may  be  transposi- 
tion but  not  inversion. 

TRIAD    SUCCESSION. 

Passing  now  to  the  study  of  the  structure  and  connection  of 
chords,  we  find  that  some  methods  present  the  whole  catalogue  of 


[  13] 

triads,  chords  of  the  seventh,  and  many  of  the  altered  accords 
and  suspensions  on  the  first  few  pages.  To  extract  from  such  a 
mass  a  clear  idea  of  any  single  species  of  chord  and  its  multiform 
manif)ulation  would  seem  a  well  nigh  hopeless  task. 

It  would  seem  more  in  accord  with  the  acknowledged  true  prin- 
ciple of  teaching  if  one  thing  at  a  time  were  taken  up  and  well 
mastered. 

As  the  triad  is  the  foundation,  the  point  of  departure  and  of  re- 
pose to  every  possible  dissonant  formation,  would  it  not  be  a  thor- 
oughly practical  idea  to  first  make  an  exhaustive  study  of  the  triad 
alone?     That  well  understood  to  be  followed  by  dissonant  chords. 

In  describing  the  structure  of  the  triad  (Maj.,  Min.,  Dim.  and  Aug.) 
and  its  different  positions,  Weitzman,  of  course,  accepts  Rameau's 
theory  of  the  common  foundation  of  the  chord,  but  not  the  doc- 
trine of  inversion,  as  applied  to  chords,  for  the  simple  rea-on  that 
it  is  physically  impossible  to  invert  any  thing  having  three  mem- 
bers, one  above  the  other.  The  structure  and  different  positions 
o'f  the  triad  are  the  same,  of  course,  but  he  esteems  it  to  be  clearer 
and  more  correct  to  speak  of  the  triad  as  in  its  fundamental  or 
third-fifth  position,  its  third-sfxth  position,  or  its  fourth-sixth  posi- 
tion. The  numerals  thus  used  convey  at  once  an  idea  of  the 
structure  and  figuring  of  the  chord. 

CnORD    PROGRESSION. 

If  the  student  is  to  readily  grasp  the  idea  of  flowing  chord-pro- 
gression, he  must  begin  with  that  idea  set  forth  in  his  exercises. 

To  this  end  the  first  exercises  should  be  upon  those  chords  most 
intimately  related,  {.  e.  the  chords  having  the  greatest  number  of 
tones  in  common  with  each  other, 

IIow  frequently  do  we  meet  with  a  bass  like  this  for  a  first  exer- 
cise : 


\^^^.=^i^^^^^:^^ 


What  proportion  of  pupils  write  out  the  appropriate  chords  the 


[14] 


first  time  without  consecutive  octaves  and  fifths  between  the  sec- 
ond   and  third  chords  ? 

The  difficulty  is  this  :  there  are  too  many  progressing  voices. 

Here  is  an  exercise  far  more  simple: 


10. 


11. 


K 


^^gj 


ezrs: 


'      -P- 


Pi 


8 


-^ 


-^=^ 


e 


TZ. 


:^2i 


^ 


Now,  in  filling  out  the  triads  above  such  a  bass,  in  which  the 
fundamental  falls  by  thirds  or  rises  by  sixths,  the  inversion,  it  will 
be  found  that  there  are  two  stationary  voices  and  only  one  pro- 
gressing voice  at  each  change  in  the  harmony. 

Let  the  tones  common  to  each  pair  of  chords  first  be  tied,  then 
lead  the  progressing  voice  to  the  nearest  unoccupied  place  in  the 
new  chord.     Kepeat  this  process  to  the  end  of  the  exercise. 

The  exercise  presents  comparatively  no  difficulty,  and  the 
chances  of  mistake  are  reduced  to  the  minimum. 

Then  the  line  of  progression  may  be  reversed,  the  fundamental 
bass  ascending  by  thirds,  or  descending  by  sixths — the  inversion, 
from  any  tonic  to  its  return,  the  upper  voices  to  be  treated  exactly 
as  before. 

Nex^  to  repeating  the  same  chord,  these  are  the  simplest  possible 
chord-successions. 

The  next  advance  should  be  to  a  chord-progression  in  which 
there  is  one  voice  to  be  tied  and  two  to  be  moved. - 

This  is  the  case  when  the  fundamental  bass  rises  or  falls  a  fifth 
or  its  inversion  a  fourth. 

We  have  examples  of  this  in  the  first  exercise  referred  to: 


[15] 


The  next  stage  of  difficulty  would  be  the  moving  of  all  the 
voices,  as  when  the  fundamental  bass  rises  or  falls  a  second.  Here 
the  general  rule  for  the  progression  would  be  to  lead  the  upper 
voices  in  contrary  motion  to  the  bass,  for  example : 


13. 


^l-^J-^^ 


It  will  be  seen  by  this  j^lan  that  the  difficulties  are  approached 
gradually.  We  will  find  that  in  this  systematic  way  the  student 
will  soon  have  learned  to  correctly  write  triad-successions  in  which 
the  bass  makes  the  following  progressions  ascending  and  descending, 
viz :  seconds,  thirds,  fourths,  fifths  and  sixths,  covering,  as  will  be 
seen,  the  principal  progressions,  in  triads,  to  be  found  in  almost 
any  piece  of  simple  character,  a  chorale  for  example. 

Of  course  the  various  positions  of  the  different  triads  and  the 
multiform  arrangements  of  the  voices  will  have  been  duly  ex- 
plained and  practiced  in  these  exercises. 

Then  in  order  to  make  a  practical  application  of  the  knowledge 
thus  acquired,  the  different  kinds  of  cadence  (plngal,  authentic 
and  complete)  should  next  be  constructed,  and  thus  equipped  with 
a  knowledge  of  triads,  embracing  their  structure,  their  means  of 
connection,  and  their  use  in  cadences,  the  subject  next  attacked 
might  very  properly  be 


[le] 


MODCLATIOil. 


Of  this  important  branch  in  the  study  of  musical  theory,  a  work, 
issued  in  Europe  some  six  or  seven  years  ago  by  one  of  the  most 
distinguished  musicians,  says  substantially  as  follows:  "  The  art  of 
modulation  is  so  difficult  to  teach  and  to  understand  that  to  pre- 
sent a  well-defined  system  of  it,  in  a  book,  is  almost  if  not  quite  an 
impossibility."  He  thus  dismisses  the  whole  matter.  Some  of  the 
text-books  present  a  series  of  modulations  already  worked  out 
which  the  pupil  is  presumably  expected  to  commit  to  memory. 

The  underlying  principles  are  not  touched  upon,  however,  and 
the  student  either  becomes  a  mere  phonograph,  able  to  modulate 
only  when  the  crank  is  turned,  or  he  stumbles  into  a  modulatory 
system  of  his  own. 

Weitzman's  general  plan  is  to  modulate  first  with  triads  alone, 
then  with  the  introduction  of  suspensions,  then  with  the  chord  of 
the  dominant  seventh,  then  with  that  of  the  diminished  seventh, 
and  finally,  with  altered  accords,  keeping  each  separate  from  the 
other  and  uniting  them  only  when  all  are  well  in  hand. 

In  the  modulations  with  triads  the  same  order  of  key-succession 
is  chosen  as  appeared  in  the  first  exercises  in  triad-succession.  It 
Vvdll  be  remembered  there  that  the  triads  related  in  the  third  first 
succeeded  each  other,  as  when  the  fundamental  bass  falls  or  rises  a 
third.  Now,  we  learn  to  modulate  to  keys  related  in  the  third,  as 
for  example  from  C  major  to  A  minor,  or  F  major  to  D  minor. 
Then  the  triads  related  in  the  fifth  followed  each  other,  as  when 
the  fundamental  bass  falls  or  rises  a  fifth. 

Now,  we  modulate  to  keys  related  in  fiftli  and  so  on,  following  up 
the  same  systematic  plan,  so  that  by  analogy,  using  each  point 
gained  as  the  step  to  the  next,  the  whole  structure  rises  gradually 
and  solidly  like  a  pyramid. 

The  principle  upon  which  these  modulations  are  effected  is  sim- 
ply to  proceed  by  related  triads  until  the  new  or  objective  key  is 
reached,  when,  if  desirable  to  come  to  a  stop,  the  complete  cadence 
is  to  be  added. 


[  17] 

The  exercises  up  to  this  point  will  have  amply  informed  the 
student  in  the  matter  of  triad-relationship,  consequently  no  ditii- 
culty  will  appear  which  has  not  been  fully  prepared  for. 

Having  effected  the  outward-bound  modulation,  the.  return  is  to 
be  accomplished  in  the  same  manner.  Then  the  t\i^o  may  be  united 
iu  a  rhythmical  period,  e.  g. 


I"erio«l. 


\ 


We  have  modulated  here  to  keys  related  in  the  third,  from  Ah 
mnjor  to  F  minor  and  v'ce  versa.  The  next  step  would  be  from  \b 
major  to  C  minor  and  vice  versa;  then  from  k.b  major  to  J)b 
major  and  return ;  then  to  Ei^  mnjor  and  return ;  then  to  B6 
minor  and  return,  the  keys  nearest  related  to  Kb  major,  and  in 
their  order  of  relationship. 

Then,  modulations  to  and  from  keys  gradually  more  distantly  re- 
lated, succeeded  finally  by  the  method  of  passing  instantly  from 
one  key  to  another  without  the  intervening  chain  of  rehitionship, 
an  idea  which  Weitzman  has  most  ingeniously  employed  in  a  re- 
markable specimen  of  muHum  in  parvo,  entitled  "900  Preludes  and 
Modulations."  The  work  is  printed  on  iioo  pages,  oblong  quarto, 
and,  while  it  is  designed  primarily  as  an  organist's  help,  it  is  de- 
\cidedly  interesting  as  a  musical  curiosity. 

Passing  over  the  chapters  on  orgail  point,  Dim.  and  Aug.  triads, 
chord  of  the  Aug.  Gth,  chords  of  the  3d,  4th  and  Aug.  Gth,  and  5th 
and  Aug.  6th,  we  come  to  the  subject  of 


HATl.MOXIC  ACCOMPANIMENT  TO  A  GIVEN  MELODY. 

I  have  been  much  gratified  at  the  skillful  method  employed  by 


.        [18] 

Mr.  Stephen  A,  Emery  in  his  Elements  of  Harmony  in  the  hand- 
ling of  this  topic.  All  the  books  do  not  go  as  thoroughly  into  thi? 
subject  as  they  ought. 

Its  mastery  is  of  great  assistance,  especially  to  the  organist  cr 
accompanist,  and  is  of  course  indispensable  to  the  composer. 

Some  methods  give  the  soprano  of  a  choral  at  once  as  a  cantus 
Jirmus  to  be  harmonized ;  others  give  the  soprano  and  bass,  leaving 
the  pupil  to  fill  out  the  middle  voices,  and  so  on. 

Best  of  all  to  begin  with,  it  seems  to  me,  is  the  method  of  har- 
monizing a  cantus  fir  miis  of  just  two  tones  at  a  time. 

Find  out  in  an  exhaustive  way  what  harmonies  may  accompany 
the  c.  f.  c'~D  for  example ;  or  any  other  second  ascending  or  de- 
scending. Then  with  a  c.  f.  of  c'e  or  c^A.  below,  or  any  other 
third,  then  a  fourth,  fifth,  etc. 

As  each  pair  of  tones  in  any  diatonic  melody  must  necessarily 
form  one  or  other  of  the  cantus  firmi  thus  practiced,  it  follows  that 
a  pupil  of  very  moderate  ability  will  be  able,  with  a  few  additional 
hints,  to  just  as  easily  harmonize  a  score  of  pairs  strung  along  in  a 
melodic  chain,  like  a  chorale,  for  example,  as  one  individual  pair. 

SUSPENSIONS. 

In  Pulestrina's  era,  suspensions  were  used  freely  but  in  connec- 
tion with  triads  only. 

The  suspension  was  always  prepared  by  a  consonance,  never  by  a 
dissonance. 

Nowadays,  not  only  consonances  but  the  free  dissonances  are 
used  in  this  capacity. 

Extremists  do  not  make  even  that  distinction,  but  use  conso- 
nances and  dissonances  alike,  without  regard  to  their  mildness  or 
harshness. 

If  we  may  use  a  mild  dissonance  to  prepare  a  suspension,  then 
to  use  a  dissonance  less  mild,  then  one  rather  harsh,  then  one 
harsher  still,  even  to  the  extremest  limit,  is  only  a  question  of  our 
endurance  or  cultivation.     Of  course  the  transition  from  one  disso- 


[19] 


nance  to  another  can  never  be  so  striking  as  from  a  consonance  to 
a  dissonance. 

Following  out  the  line  of  triad  development  set  forth  by  Weitz- 
man,  the  method  is  to  first  introduce  suspensions,  like  Palestrina 
and  his  contemporaries,  in  connection  with  triads  alone,  and  accord^ 
ing  to  the  rules  of  those  days,  which  are  regarded  still  as  classical, 
viz :  the  jDreparation  of  the  suspension  consonant,  the  attack  of  the 
dissonance  accented,  the  resolution  a  diatonic  degree  downward. 


15. 


e.g. 


'm^ 


-A^ 


m^ 


As  already  observed  in  another  part  of  this  paper,  Frescobaldi, 
whose  epoch  began  a  little  later  than  that  of  Palestrina,  was  bold 
enough  to  resolve  some  dissonances  upward. 

The  custom  has  continued  and  broadened  and  upon  this  practice 
Weitzraan  has  formulated  the  following  theory,  viz:  A  dissonance  is 
the  melodic  retardation  of  a  consonance ;  the  appearance  of  a  dissonance 
creates  the  expectancy  of  a  consonance  ;  the  melodic,  i.  e.  degree-wise  resolu- 
tion of  that  dissonance  into  a  consonance  satisfies  the  musical  instinct  at 
once ;  the  appearance  of  the  consonance,  as  a  resolution  of  the  dissonance,  is 
of  primary  importance,  the  pirection^  taken  hy  the  dissonance  in  its  passage 
to  the  consonance  is  secondary ;  consequently  it  is  as  logically  correct  to 
resolve  the  dissonance  upward  as  it  is  to  resolve  it  downward. 

To  illustrate,  take  the  suspension  of  the  second,  thus  : 


16. 


m 


A 


Z2: 


_<^ 


Now  to  follow  the  old  rule  would  oblige  us  to  resolve  the  upper- 
voice  downward,  thus: 

17. 


m. 


.    [  20  ] 

This  would  be  false  because  a  dissonance,  with  the  exception-  of 
the  suspension  of  the  seventh  and  the  ninth,  can  not  appear  as  the 
retardation  of  a  tone  already  present.  That  would  be  a  self-contradic- 
tion. 

In  this  example  we  hear  the  A  already  during  the  dissonance, 
consequently  it  can  not  be  that  sound  which  the  dissonance  B,  an- 
ticipates. 

No,  the  resolution  must  take  place  degree-wise,  /.  e.  scale-wise,  to 
some  other  consonant  of  A,  either  C  or  C  sharp,  thus: 


Or  the  two  tones  may  resolve  to  another  consonant  in  contrary 
motion,  thus: 


10. 


I  have  added  a  third  voice  (E)  to  conceal  the  empty  character  of 
the  minor  forth. 

The  perfection  of  the  theory  thus  hastily  demonstrated  will  ap- 
pear again  in 

CHORDS    OF    THE    SEVENTH, 

at  which  we  will  now  briefly  glance. 

Rameau  was  also  the  author  of  the  theory  that  the  different  po- 
sitions of  a  chord  of  the  seventh,  as  well  as  those  of  a  triad,  were 
all  based  on  a  single  fundamental  harmony,  whereas,  before  his 
time,  it  had  been  the  custom  to  give  a  distinct  name  to  each  and 
every  harmonic  combination. 

Imagine  such  a  method  of  teaching  harmony  now-a-days!  The 
only  parallel  that  occurs  to  me  is  the  method  of  writing  the  Chi- 


*We  may  dislike  to  break  a  rule  or  make  a  breach  in  a  theory,  but  we  are  as- 
sured by  its  author,  as  well  as  by  time-honored  usage,  that  the  bass,  in  these 
particular  cases,  is  inherently  weighty  enough  to  set  aside  both  rule  and  theory. 


[21  ] 

nese  language  with  its  20,000  characters,  as  compared  with  our 
alphabetical  system. 

Kameau  certainly  merits,  for  his  remarkable  theory,  the  grati- 
tude of  posterity  to  the  remotest  bounds  of  time. 

To  recognize  the  theory  of  inversion  in  connection  with  chords 
of  the  seventh,  however,  would  be  |ust  as  inconsistent  as  it  is  with 
triads. 

It  would  certainly  appear  more  practical  to  give  the  different 
positions  a  name  v/hich  would  at  the  same  time  describe  the  struc- 
ture of  each  position. 

After  the  fundamental  position  the  names  fifth-sixth  position, 
third-fourth  position,  and  second-fourth  position,  would  indicate 
the  essentially  different  features  of  each  position,  and  the  figuring 
necessary  to  distinguish  them  from  each  other  better  than  the 
names  "  1st,  2d,  and  3d  inversions." 

In  explaining  the  principal  resolution  of  the  Dom.  7th  accord, 
(.liat  to  the  tonic  triad,  Weitzman  proceeds  in  this  manner. 

Having  written  down  the  Dom.  7th  accord,  we  are  first  to  tie  any 
note  common  to  the  chord  of  resolution  or  tonic-triad,  thus : 

20. 


■m- 


Then  the  dissonance  (F)  is  to  be  resolved. 

This,  like  all  other  dissonances,  must  resolve  degree-wise  up- 
ward or  downward  to  a  member  of  the  triad  of  resolution  (  ceg  here) 
Here  is  to  be  repeated  the  theory  concerning  dissonances  already 
given  in  connection  with  suspensions.  No  dissonance  can  be  re- 
solved to  a  tone  already  present,,  hence  the  seventh  here  can  not 
rise  to  G,  thus : 

21. 

^    22Z 


m 


''Examples  20  to  26  inclusive,  to  be  played  an  octave  higher. 


[22] 

But  must  fall  to  E  since  that  is  the  only  other  tone  of  the  triad  of 
resolution  (  ceg  )  distant  a  single  degree,  thus : 

22. 


m- 


-(^^ 


The  ildnl  in  the  7th  accord  (B)  being  the  leading-tone  will  follow 
its  natural  progression  (subject  afterward  to  an  exceptional  priv- 
ilege) to  the  tonic  thus  : 


23. 


The  fifth  (D)  may  ascend  to  E  or  descend  to  C,  the  tonic.  The 
latter  is  better,  as  on  general  principles,  it  is  better  to  double  the 
Jandanicntal  than  any  other  member  of  a  chord,  thus: 

24. 


This  resolution  yields  the  foui-th-sixth  position  of  the  triad;  if 
the  fundamental  position  were  more  desirable,  the  fundamental 
of  the  seventh  accord  (G),  being  a  consonant  and  therefore  freer 
in  its  progression,  may  be  led  to  the  fundamental  of  the  triad  of 
resolution,  thus: 

25. 


:g: 


S53 


Again,  as  the  triad  lacks  its  fiftli,  and  as  the  third  of  the  domi- 
nant seventh-accord,  which  is  always  the  leading  tone,  appears  as  a 
rrudillc  voice,  it  may  be  led  downward  so  as  to  fill  out  the  lacking 

fifth  ill  the  triad,  thus  : 

26. 


[23] 

Of  course  the  treatment  would  be  better  now  if  the  bass  were  to 
be -led  in  contrary  motion  to  the  other  voices,  thus: 

27. 


In  the  resolution  of  the  so-called  first  inversion  or  fifth-sixth  po- 
sition, as  well  as  in  all  the  different  positions,  the  very  same  princi- 
ples obtain.  The  pupil  is  not  asked  to  commit  to  memory  a 
formula  of  resolution  for  each  one,  always  dry,  tiresome  work,  but 
to  understand  the  simple  principles  and  apply  them. 

Then  should  follow  an  exhaustive  systematic  study  of  the  differ- 
ent ways  in  which  the  Dom.  seventh-accord,  in  its  different  posi- 
tions, and  placings  of  the  voices,  may  enter  after  the  triads  on 
each  degree  of  the  scale,  taking  them  in  rotation,  for  example: 


-^ 


1^21 


d^: 


-^       -^ 


^^^mi 


C        07 


07 


e        G7 


F  07 


S 


:!H: 


22: 


11=1 


^ — ep- 


Z2: 


-L      I 


:^ 


a        «  7 


B  «7 


Then,  a  certain  fixed  triad  should  be  selected  and  an  exhaustive 
study  made  of  the  methods  of  entering  after  this  one  triad  the 
Dom.  seventh-accords,  in  the  different  positions  and  placings  of  the 
chord,  of  every  other  mode.  Here  are  a  few  by  way  of  illustra- 
tion : 


[24] 

S9. 


|^-S-^^^-:-^^l^- 

-s=t-^^ 

!>:g=] 

6- 

ur 


fttT 


tJ 


JE^ 


7^ 


-s^ 


iH 


t^s^ 


^h 


li 


[?4 
_5L 


^5 


etc. 


-3^- 


1^1 


r  7 


Etr7 


The  student  learns,  hereby,  the  use  of  the  chord,  its  entrance 
and  exit,  and  its  function  in  modulation;  for,  if  to  any  one  of 
these  examples  wc  add  a  suitable  cadence,  the  modulation  to  a  new 
key  will  be  complete. 

Let  us  next  glance  at  the  secondary  resolutions  of  the  Dora, 
seventh-accord. 

In  connection  with  this,  I  desire  to  call  your  attention  to  a  sim- 
ple method  of  testing  the  correctness  of  the  resolution  of  any  dis- 
sonant harmony. 

Suppose  we  wish  to  resolve  the  same  Dom.  seventh  accord  to  the 
triad  of  D  minor. 

After  havin<;  written  down  the  seventh  accord  thus: 


m 


"Write  down  the  letters  of  the  triad  of  resolution  underneath,  thus: 


[  25  ] 

Xow,  strike  out  the  letters  of  the  triad  which  are  found  in  the 
seveuth  accord  thus : 


The  letters  thus  canceled  indicate  the  connecting-tones  between 
the  two  chords.     These  are  to  be  tied  thus  : 


33. 


;b=s^ 


7) 

Then  the  remaining  voices  of  the  seventh  accord  (G  and  B)  are 
to  be  led  degree-wise  to  the  letter  not  canceled  (A)  thus : 

3i. 


?^2222Z: 


T) 


Take  this  in  dispersed  harmony  and  it  will  show  just  how  the 
voices  are  to  be  led  in  resolving  g'bdb'  ta  D  F  A,,  as  before,  thus 


33. 

f)         •    ^ 

»^ 

1     /        ^-D  - 

y      c:^ 

^\~^-^- 



1^   ^^_ 

/«>• 

' — " 

m — 

h^  n 

<S?a 


Let  us  try  the  same  process  in  resolving  the  same  Dom,  seventh 
accord  to  the  trfcid  of  E  minor,  for  example : 


36. 


e  {^  S» 


[26  1 


Again,  in  a  resolution  to  B  major,  thus  : 


37. 


Ip-i^^ 


Please  note  that  each  moving  voice  progresses  degree-wise,  ex- 
clusively, in  the  secondary  resolution. 

Note  here  that  the  seventh  itself  is  resolved  upward,  despite  the 
rule  to  the  contrary ;  yet  the  ear  is  satisfied,  or  would  be,  were  the 
cadence  added.  These  secondary  resolutions  are  also  to  be  em- 
ployed in  new  modulations. 

The  same  test  may  be  applied  also  to  deceptive  cadences. 

Suppose  that  we  desire  to  connect  the  dominant  seventh  accords 
GEDF  and  EZ/GB&nb  •  Write  down  the  first  chord  in  any  desired 
position,  then  the  letters  of  the  second  chord  underneath,  and 
strike  out  those  found  common  to  both,  then  tie  the  note  which 
the  cancelled  letter  stands  for  and  finally  lead  the  remaining  voices 
degree-wise  to  their  places  in  the  new  chord  thus  : 

3S. 


M" 


122: 


els  bt2:d!2: 

If  the  succession  can  be  accomplished  without  consecutive  fifths 
or  octaves,  or  unmelodic  voice-leading,  it  may  be  accepted.  This 
simple  method  will  be  found  an  infallible  test  as  to  the  correctness 
or  legitimateness  of  any  dissonant  progression  or  resolution  what- 
soever, and  if  the  writings  of  our  composers  can  not  be  justified  by 
it,  then  their  work  needs  revision. 

Passing  over  an  elaborate  treatment  of  secondary  chords  of  the 


[27] 


seventh,  including  that  of  the  diminished  seventh  and  its  office  in 
modulation,  I  wish  to  present  a  method  of  writing  a  chromatic 
succession  of  diminished  seventh  accords,  a  procedure  which  is 
sometimes  perplexing. 

If  the  passage  be  an  ascending  one,  the  chords  should  be  so 
written  as  to  cause  the  fundamental  to  rise  a  major  fifth  or  fall  a^ 
minor  fourth,  for  example  : 


30. 


-^7^ 


-^te-^eSEiqfe^^^S 


'^^^Xi,^- 


m 


In  descending,  the  fundamental  should/t//^a  mojor  fifth  or  rise  c/ 
minor  fourth. 

Wiitten  in  this  manner,  each  pair  of  chords  will  have  two  voices- 
which  do  not  change  their  staff-degree,  thus  giving  us  (see  curved 
lines)  an  ideal  connection. 

A  few  words  concerning  the  so-called  chords  of  the  ninth,  elev- 
enth, and  thirteenth,  and  altered  chords,  and  I  shall  have  finished. 

Many  are  the  rules  and  hints  given  for  the  treatment  of  these 
so  called  chords,  when,  if  they  are  but  recognized  as  chords  of  the 
seventh  over  an  organ-point,  the  rules  already  mastered  in  the 
study  of  those  chords  will  bo  found  to  apply  perfectly  and  the  dif- 
ficulties to  vanish  instantly. 

The  so-called  chord  of  the  minor  ninth  is  simply  a  diminished 
seventh  accord  over  an  organ-point  on  the  dominant. 

The  treatment  is  precisely  the  same  as  would  be  applied  to  the 
Dim.  seventh  accord  alone,  for  example  : 

40. 


^^^^Efe^a 


=^s- 


:8; 


W^ 


P^ 


ete 


[28] 

The  so-called  chord  of  the  major  ninth  is  an  organ-point  on  the 
dominant,  upon  which  appears  the  seventh  accord  found  on  the 
leading-tone  in  a  major  mode,  e.  g. 

41. 


w 


fen 


p^ 


Z2: 


-^-«-s^ 


Here  is  another  position  of  these  same  chords,  with  the  third  of 
the  upper  chord  omitted,  which  is  called  an  inversion. 


The  apparent  inversion  is  caused  by  the  sustained  tone  appear- 
ing as  a  middle  voice.     It  is  an  organ  point  as  before. 

If  we  apply  the  theory  of  inversion  here,  the  chord  of  the  major 
ninth,  in  one  position,  would  assume  the  following  striking  form: 


4:1. 


m 


^ 


The  so-called  chord  of  the  eleventh  is  simply  an  organ-point  with 
the  dominant  seventh-accord  over  the  tonic,  e.  g. 


i 


44. 


s 


'^2: 


22: 


Z2: 


22: 


IS 


1221 


[29] 


The  so-called  chord  of  the  thirteenth  is  an  organ-point  with  two 

sustained  tones,  the  tonic  and  dominant,  or  the  dominant  may  be 

omitted.     The  upper  chord  is  either  a  diminished  seventh  accord 

or  the  seventh  accord  found  on  the  leading-tone  in  a  major  mode, 

for  example: 

45. 


7)  -^-     -&"- 


B£SES 


I>ominnnf  omitted,  nlso 
11143  'Ml  in  tlie  upper  eliurd. 


^Eg=g^=g 


As  a  final  proof  of  the  stability  of  this  theory,  here  is  an 
organ-x^oint  which  introduces  each  of  these  so-called  chord-forma- 
tions : 

J  -.     ^! ! .—-4 \ . — 4- 


i^ia 


ALTERED  ACCORDS. 

The  four  kinds  of  triad  found  in  the  major  and  different  forms 
of  the  minor  mode  are  major,  minor,  diminished  and  augmented. 
Every  other  triad  should  be  classed  as  an  altered  triad. 

Just  so,  only  those  seventh-accords,  which  are  common  to  the 
major  and  minor  modes,  should  be  recognized  as  fundamental 
seventh-accord  formations ;  all  others  should  be  classed  as  altered 
seventh-accords.     The  method    of  conferring  special  names  upon 


[  30'  ] 

any  of  these  artificial  formations  is  only  going  back  to  the  prac- 
tice of  anti-Rameau  days.  There  is  no  practical  advan  age  in  it, 
and  it  is  just  so  much  of  a  blemish  on  the  perfection  of  any  sys- 
tem. 

The  most  important  point  is  to  recognize  from  what  harmonies 
they  are  derived  and  thereby  learn  how  they  are  to  be  treated. 

They  arise  most  frequently  through  a  desire  to  better  express 
the  melodic  leading  of  the  voices,  for  example  : 


47. 


m^^3^^ 


^ 


m 


22: 


■1^ 


'.  >r>.. 


r^z. 


Here,  in  the  soprano,  the  E  sharp  expresses  a  more  definite  lead- 
ing back  to  F  sharp  than  would  F.  Just  so  the  Gr  sharp,  in  the  bass, 
leads  more  decisively  back  to  A  than  would  A  flat,  the  tendency 
of  which  latter  would  be  ta  G. 

The  combination  here,  then,  is  C  E  sharp  G  sharp.  If  we  cancel 
the  accidentals,  we  shall  quickly  see  the  original  triad,   ceg- 

Here  is  a  very  effective  introduction  of  an  altered  seventh-ac- 
cord : 

48. 


iaSfeip 


HH 


The  E  sharp,  in  the  tenor  expresses  a  melodic  leading  to  F  sharp 
the  G  sharp,  in  the  alto,  tends  toward  A,  and,  as  the  soprano  is  oi;  i'.s 
way  to  A,  via  B,  the  accidental  formation  is  C  E  sharp  G  sharp  B. 
Cancel  the  accidentals,  and  we  discover  the  original    seventh-ac- 

COrCl,      CEGB  • 


C  31  ] 

The  altered  accords  are  more  limited  in  their  progressions  than 
their  derivatives,  and  the  only  semblance  of  a  rule  that  can  be 
given  for  the  progression  of  these  chromatically  altered  notes  is  to 
follow  their  natural  tendency, — the  sharps  tending  degree-wise  up- 
ward and  the  flats  degree-wise  downward, — provided  always  that  the 
corresponding  voices  in  the  derivative  chord  could  make  the  same 
progressions. 

In  conclusion,  I  would  say  that  I  am  conscious  of  having  com© 
far  short  of  the  ideal  paper  I  imagined  I  would  write  when  the  title 
was  formulated.  I  have  not  expressed,  as  I  intended  to,  any  thing 
of  my  appreciation  and  admiration  of  very  much  of  the  work  done 
in  the  host  of  text  books  which  I  have  examined.  In  these  re- 
searches I  have  been  extremely  gratified  at  the  growing  concise- 
ness and. accuracy  in  definitions,  and  the  simplicity  of  the  methods 
employed,  especially  in  later  works.  "We  are  certainly  nearing  the 
musical  millennium  for  teachers  and  students  of  harmony.  "What 
we  need  and  what  is  gradually  being  shaped  for  us  is  a  universal 
method,  free  from  contradictions,  systematic,  yet  elastic  enough  to 
adapt  itself  to  the  wants  and  peculiarities  of  each  individual  pupil. 
May  that  era  soon  dawn  upon  us  I  E.  M.  Bowman. 


'  I 


p 


9 


uvsiGAL  worn  :iim  s?  the  mmm  of  mi  mi 


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-H  0®M^^  M^MPi 


Oaylord  Bros. 

Makers 

Syracuse,  N.  Y. 

PAT.  JAM.  21.  1808 


MT50.B6 

C037327475 

U  C.  BERKELEY  LIBRARlis' 


M 


CD373E7M7S 


DATE  DUE 


Music  Library 

University  of  California  at 
Berkeley 


